How to solve and plot system differential equation...

How to solve this problem? I want to display plot of differential equation system

Thank you :)

why dsolve solution sometimes shows as implicit wh...

Sometimes dsolve returns solution as implicit, even when not using the `implicit` option. For example

```restart;
ode:=diff(y(x),x)=(x*y(x))^(1/2):
sol:=dsolve(ode,y(x));```

Gives

Which is the same result if I had used 'implicit'.

Is there a way to tell dsolve not to do this? is it becuase it can't solve for y(x) from the above?

Maple 2017.1

how can i draw a plot rkf45 ...

i want to draw plot Y[1] . but i cant. thank you

restart;
with(LinearAlgebra); Digits := 15; with(plots); with(Optimization);;
NewM := Matrix(5, 5, [[4119700.0000, 0., 0., 0., 0.], [0., 175900.0000, 0., 0., 0.], [0., 0., 52796., 0., 0.], [0., 0., 0., 2002900.0000, 0.], [0., 0., 0., 0., 21711.]]); NewK := Matrix(5, 5, [[18278000.0000, 0., 0., 0., 0.], [0., 8478500.0000, 0., 0., 0.], [0., 0., 3874800.0000, 0., 0.], [0., 0., 0., 494710000.0000, 0.], [0., 0., 0., 0., 7707500.0000]]); L := Vector[column](5, [400689.480747934, 36882.2103608425, 24223.1756570268, 7197.48654698287, 5007.64668721342]); V := Vector[column](5, [4.43679672962542, 48.2014976972537, 73.3916065733549, 246.999805581163, 355.012621460930]);
Phi := Matrix(5, 5, [[1., 1., 1., 1., 1.], [1.96506022575420, 1.62041320563413, 1.42204109823483, 0.548765310483432e-1, -.795724394004826], [9.21473910149806, 2.36597630710861, -.837387679777313, -8.23805381555997, 0.930594200639915e-1], [10.5672146719479, 1.26937656539014, -.710851068914949, 12.5801876194058, -0.564138989400088e-1], [12.4282433098880, -2.02516824673162, .481291188486771, -1.71479964168293, 0.513709374343217e-2]]);
NS := ImportMatrix("D:/tabas.txt", datatype = float[8]);
t_NS := NS[() .. (), 1];
acc_NS := NS[() .. (), 2];
plot(NS, t = 0 .. 4.5, size = [800, 400]);
acc := unapply(CurveFitting:-Spline(t_NS, acc_NS/(9.81), t, degree = 1), t);
eq := seq(diff(x[i](t), t\$2)+(2*0.5e-1)*sqrt(V[i])*(diff(x[i](t), t))+V[i]*x[i](t) = L[i]*acc(t)/NewM[i, i], i = 1 .. 5, 1);
ic := [seq({x[i](0) = 0, (D(x[i]))(0) = 0}, i = 1 .. 5, 1)];
sol := seq(dsolve({eq[i], ic[i][]}, numeric, output = listprocedure), i = 1 .. 5, 1);
Z := `<,>`(seq(sol[i][2], i = 1 .. 5));
#Y := Phi . Z;
#odeplot(Y[1], t = 0 .. 10);
tabas.txt

1.mw

how can i draw odeplot this numeric dsolve...

i want to draw plot Y[1] . but i cant. thank for you

i want to take this equation

restart;
with(LinearAlgebra); Digits := 70; with(plots);

K := Matrix(5, 5, [[18278000.0000, 0., 0., 0., 0.], [0., 8478500.0000, 0., 0., 0.], [0., 0., 3874800.0000, 0., 0.], [0., 0., 0., 494710000.0000, 0.], [0., 0., 0., 0., 7707500.0000]]); M := Matrix(5, 5, [[4119700.0000, 0., 0., 0., 0.], [0., 175900.0000, 0., 0., 0.], [0., 0., 52796., 0., 0.], [0., 0., 0., 2002900.0000, 0.], [0., 0., 0., 0., 21711.]]); L := Vector[column](5, [400689.48, 36882.21, 24223.175, 7197.4865, 5007.6466]); V := Vector[column](5, [4.4368, 48.201, 73.39160, 246.999, 355.012]);
NS := ImportMatrix("D:/tabas.txt", datatype = float[8]);
t_NS := NS[() .. (), 1];
acc_NS := NS[() .. (), 2];
plot(NS, t = 0 .. 4.5, size = [800, 400]);
acc := unapply(CurveFitting:-Spline(t_NS, acc_NS/(9.81), t, degree = 1), t);
eq := seq(diff(x[i](t), t\$2)+(2*0.5e-1)*sqrt(V[i])*(diff(x[i](t), t))+V[i]*x[i](t) = L[i]/M[i, i], i = 1 .. 5, 1);
ic := [seq({x[i](0) = 0, (D(x[i]))(0) = 0}, i = 1 .. 6, 1)];
res := evalf(seq(dsolve({eq[i], ic[i][]}, numeric, method = rkf45), i = 1 .. 5, 1));
Z := `<,>`(res[1], res[2], res[3], res[4], res[5]);
Y := Phi . Z;
#odeplot(rhs(Y[1]), t = 0 .. 4)

import file text

tabas.txt

how can i solve maximize of numerical dsolve...

restart;
res := dsolve({25*(diff(y(t), t, t))+4*(diff(y(t), t))-3*y(t) = cos(3*t), y(0) = 0, (D(y))(0) = 1}, numeric, method = rkf45);
with(Optimization);
Maximize(res, t = 0 .. 4);

"unable to store %1 when datatype=%2", -9.65986559...

hello...how i can remove this error?

thanks

 (1)

 (2)

how can i draw the plot of solution of Runge–Kutta...

how can i draw the plot of solution of Runge–Kutta methods

@rkt4.mw

how can i solve coupled differential of equation...

how can i solve coupled differential of equation with rkf or another method

maple.mw

A1 , A2, A3 ??

how to dsolve of a equation ...

i want to dsolve frome this equation . but i cant

1.mw

How to solve BVP with singularities?...

Dear friends,

I have to solve the BVP of the following type:

(x-1)*y''(x)+y'(x)=1+x, y(0)=1, y(1)=1

Expressing the highest derivative (y''(x)), we get a singularity at x=1.

So, as recommended, the method bvp[middefer] (or bvp[midrich]) is used:

`dsolve({(x-1)*diff(y(x), x\$2)+diff(y(x),x) = 1+x, y(0)=0, y(1)=1}, type = numeric, method = bvp[middefer], y(x), 'output' = Array([seq(k/10, k=0..10)]), 'abserr'=1.0e-3, 'maxmesh'=100)`

Maple generates the following error:

Error, (in dsolve/numeric/bvp) unable to achieve requested accuracy of 0.10e-2 with maximum 100 point mesh (was able to get 0.82e3), consider increasing `maxmesh` or using larger `abserr`
But as I increase maxmesh, the achievable accuracy (reported in "(was able to get XXX)") decreases:

for

maxmesh = 200: 0.19e4

maxmesh = 500: 0.54e4

maxmesh = 1000: 0.12e5

maxmesh = 5000: 0.73e5

and so on.....

How to solve this equation with desirable accurancy and usage of Array as output?

problem with an ode...

i want to solve an ode , but maple return an integral in result, how can i have an answer?

 > restart:
 > eq:=1/(x*y^(2/3))*8.620689655172415*10^(-16)*(-3.11*10^23*x^2*y^(7/6)-3.92*10^19*y^(25/6)+2.14545039999999*10^29*(0.0108*exp(-45.07/y)+exp(-19.98/y^(1/3)-0.00935317203476387*y^2)))/(x+0.015*y^(1.2));
 (1)
 > eq:=subs(y=y(t),eq):
 >
 > ans:=dsolve(diff(y(t),t)=eq);
 (2)
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odeplot of a complex function ...

hello,

i went to plot a complex numerical solution , i used odeplot but did not work

Thank you very much

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How to numerically solve differential equation?...

I'm trying to numerically solve the differential equation: y' = -2xy + 1. Naturally, I come across the non-elementary integral of e^(x^2). By hand, I used a 2nd degree MacLaurin polynomial to get y = xe^(-x^2) + x^3/3e^(-x^2)+x^3/6e(-x^2).

How do I use Maple to numerically solve this, with step sizes of h=0.1 and h=0.05 and plot them?

How to Graph Overlaying Plots With No Errors?...

I am trying to plot some graphs for a differential equations class. I need to plot two equations (soln1a, soln1b1) in one graph, with the two curves overlayed on each other. I am trying to plot them on a graph named "gr1c". The error I get says "Error, (in plots/multiple) empty plot". Clicking on the error results in a webpage saying that "There is no help page available for this error".

When I plot each equation separately, there are no errors. The graphing command that works for soln1a is

gr1a:=plot(rhs(soln1a),dom1,color=blue);

and the graphing command that works for soln1b1 is

gr1b1:=plot(rhs(soln1b_1),dom1,color=purple);

My code is as follows. I would greatly appreciate any help ASAP to remove the error. Thank you!

with(plots):with(DEtools):

K:=9;
deG:=diff(theta(t),t,t) + mu*diff(theta(t),t)+K*sin(theta(t))= 0;
deL:=diff(theta(t),t,t) + mu*diff(theta(t),t)+K*theta(t)= 0;
Iv:=theta(0)=0.75, D(theta)(0)=2.0;
dom1:=t=0..10;
soln1a:=dsolve({eval(deL,mu=0),Iv});

soln1b_1:=dsolve({eval(deL,mu=1),Iv});

gr1c:=multiple(plot[soln1a,soln1b1],dom1,color=[blue,purple]);

Error, (in fprintf) number expected for floating p...

hello...i have a problem with this program.

I want to save the result(y,u(y)) in a text or another format file, but I encounter with this error message:

Error, (in fprintf) number expected for floating point formatBVP.mw

restart:

A1:= 5.5:  n:= 0.59:  A2:= 11818.:  h0:= 0.402e-3:
L:= .1:  dpx := -11823.9:  uc:= 0.44e-2:

ODE:= (A3,y)->
(h0^(n+1)*L/sqrt(n)*(A1*exp(sqrt(n)*y/L)-A2*exp(-sqrt(n)*y/L))+dpx*y*h0^(n+1)+A3*(h0)^n)^(1/n)
;

 (1)

ODEINT:= proc(A3)
option remember;
local y;
evalf(Int(ODE(A3,y), y= 0..1, epsilon= 1e-7)) - uc
end proc:

ReINT:= proc(A3x, A3y)
Digits:= 15:
Re(ODEINT(A3x + I*A3y))
end proc:

ImINT:= subs(Re= Im, eval(ReINT)):

Digits:= 7:
a3:= fsolve([ReINT, ImINT]);

 (2)

A3:= Complex(a3[]);

 (3)

Solve as IVP:

Digits:= 15:
sol:= dsolve({diff(u(y),y) = ODE(A3,y), u(0)=0}, numeric, range=0..1,  output=listprocedure):

plots:-odeplot(
sol, [[y, Re(u(y))], [y, Im(u(y))]], y= 0..1,
legend= [real, imag], labels= [y, u(y)]
);

 >